Civilization – How to get a build recommendation for city after it was building wealth/research/culture

Unfortunately, I do not know exactly how much you must culturally dominate a city for it to switch. That number may well depends on your difficulty level.

However, I think I can help answer your implied question: This city is more culturally mine. Why hasn't it switched to my empire?

First be sure city switching due to culture is turned on.

I assume it is, but this is an option you can set before the game, so its worth mentioning.

The threshold might not be 51% This is what you supposed, and I agree this might be true. Until someone else chimes in with a number (or several for difficulty) lets assume something else is wrong...

Culture switches are not immediate.

The city will usually have at least one cultural revolt first, i.e. both you and the current owner of the city will see an event like "A [Spanish] revolt is taking place in [City]." This is a great sign for you, and means that you passed the threshold; the city would switch to your empire fairly soon if it had no troops in it. This has the unfortunate consequence that...

The current owner can put troops in the city to slow you down

The longer the city is in revolt in the name of your culture, the more likely it is to switch. So naturally, if the revolt is suppressed by, say, more troops, its less likely to be successful. I think with enough troops the revolts can be prevented altogether. I'm not sure of this, or whether a city can switch without revolting first.

Troops are the only way I can remember the current owner being able to fight you, but there may be others options I can't remember, like particular government choices or wonders?

Consider destroying the troops with espionage

If the troops can slow down the process, then get rid of them. You sound like you want to take the city without war, so spies are the option you have left. But, if you don't care whether you go to war or not...

Consider taking the city with military

If I recall correctly, a city that prefers you culturally will be "liberated" rather than "conquered". Unfortunately, this has the same problem you asked about taking the city cultural: how much is enough? I'm not sure, but I believe if they have revolted for you then its enough.

Liberating a city is effectively "this city is supposed to be mine, the people welcome me", I am certain its what happens when you retake a city you founded but lost, and has great effects:

• The city does not lose a population due to being "conquered".
• The people do not revolt, but begin working immediately.
• Buildings are more likely to survive the transition. (Perhaps all of them do?)
• (Does not apply to your situation but...) The cultural border the city had when you last controlled it are restored.

As a final note, if you could liberate a city, and a third civilization takes the city, they immediately have the option of "returning" it to you.

I feel like I've missed something, I will add it later if I think of it.

Yes, city defenses heal over time. If you bombard a city and lower its defense, and then leave it alone for a while, the damage will be repaired as turns pass.

Base city defense is a factor of the city's culture. (see "How do I increase my city's defense" in this Civ4 FAQ) If you increase the base city defense with things like City Walls, then the maximum amount of city defense increases. If you bombard the city enough, the defensive bonus from city buildings/wonders will be lost, but the building/wonder will not be destroyed. Eventually, the city will heal its defenses back to the maximum.

The defensive bonus for the city is calculated as follows:

• For each culture level the city has, gain 20% up to a max of 100%
• If walls/castle are present, and the normal maximum defense is less than the amount this improvement specifies, replace it with the defensive bonus for the improvement, so long as a pre-gunpowder unit is selected.
• If Chichen Itza is in effect, add 25% to the city defense percentage

I tested this by rushing gunpowder and building walls in a city that normally would have 40% city defense (ie, culture level 2), then gifting the city to an enemy player and declaring war. I could toggle between highlighting my longbowmen and my musketmen, and the defensive bonus would be 50% when the longbowmen were selected, and 40% when the musketmen were selected.

I believe the applied defensive bonus for units in a city is the combination of the current city defense rating, plus the defensive rating from the tile, plus any modifiers that the unit has (ie, a defensive unit with the City Garrison ability). Even if you take the city defenses out of the equation, you'll still have to contend with those other bonuses.

I believe Spies can influence this as well, although it's been a while and I can't recall what was in the base game versus what was added in the expansions.